Thank you for your interest in BF Auction Plus.
I encourage you to download the free trial version so you can try the software out on your own site and see if it will meet your needs. Simply fill out the "Download FREE trial" form on our homepage (in the blue box on right).

Regarding your questions:
1. Currently auction items that have ended are still visible to everyone, with the buy now or bid now button removed. The winner of the auction item will also see the PayPal payment button. If you wanted to hide completed auctions, it would just require a minor tweak to the model for that view, for example /components/com_bfauction_plus/models/bfauction_plus.php

$where = ' WHERE (b.state IN (1))';

//could be changed to something like
$where = ' WHERE (b.state IN (1) AND b.winEmailSent=0)';

2. Yes there are various emails sent by the software, you can set up an email template for each and customize the message.